Resumen de On the quantum affine vertex algebra associated with trigonometric R-matrix

Slaven Kožic

• We apply the theory of ϕ-coordinated modules, developed by H.-S. Li, to the Etingof–Kazhdan quantum affine vertex algebra associated with the trigonometric R-matrix of type A. We prove, for a certain associate ϕ of the one-dimensional additive formal group, that any (irreducible) ϕ-coordinated module for the level c∈C quantum affine vertex algebra is naturally equipped with a structure of (irreducible) restricted level c module for the quantum affine algebra in type A and vice versa. In the end, we discuss relation between the centers of the quantum affine algebra and the quantum affine vertex algebra.